 Torsion-free abelian group

An abelian group in which no nonzero element has finite order. Free abelian groups are torsion-free, but torsion-free groups need not be free, as the additive rationals show. This algebraic meaning differs from the torsion-free connection in differential geometry.

A **torsion-free abelian group** is an important concept in group theory, a branch of abstract algebra.